@article{ZHOU2020103824,
title = "Actively controllable topological phase transition in homogeneous piezoelectric rod system",
journal = "Journal of the Mechanics and Physics of Solids",
volume = "137",
pages = "103824",
year = "2020",
issn = "0022-5096",
doi = "https://doi.org/10.1016/j.jmps.2019.103824",
url = "http://www.sciencedirect.com/science/article/pii/S0022509619307033",
author = "Weijian Zhou and Bin Wu and Zhenyu Chen and Weiqiu Chen and C.W. Lim and J.N. Reddy",
keywords = "Actively controllable, Interface mode, Piezoelectric rod, Topological phase inversion",
abstract = "By employing periodic electrical boundary conditions, an innovative method to generate actively tunable topologically protected interface mode in a “homogeneous” piezoelectric rod system is proposed. Made of homogeneous material and with uniform structure, each unit cell of the piezoelectric rod system consists of three sub-rods forming an A-B-A structure, where the two A sub-rods have the same geometry and electric boundary conditions. It is discovered that the switch of electrical boundary conditions from A-closed and B-open to A-open and B-closed will yield topological phase inversion, based on which topologically protected interface mode is realized. When capacitors CA and CB are connected to the electrodes of sub-rods A and B, respectively, a variety of physical phenomena is observed. On one hand, varying the capacitance in a certain path leads to topological phase transition. On the other hand, different variation paths of the capacitors give rise to different locations of topological phase transition points. This discovery allows the eigenfrequency of the topologically protected edge mode thus formed be actively controlled by appropriately varying the capacitance. The active topological protected interface mode may find wide engineering applications that require high sensitivity sensing, nondestructive testing, reinforcing energy harvesting, information processing, and others."
}
@article{GRENDYSA20171,
title = "MBE growth of Topological Isolators based on strained semi-metallic HgCdTe layers",
journal = "Journal of Crystal Growth",
volume = "480",
pages = "1 - 5",
year = "2017",
issn = "0022-0248",
doi = "https://doi.org/10.1016/j.jcrysgro.2017.10.003",
url = "http://www.sciencedirect.com/science/article/pii/S0022024817306048",
author = "J. Grendysa and G. Tomaka and P. Sliz and C.R. Becker and M. Trzyna and R. Wojnarowska-Nowak and E. Bobko and E.M. Sheregii",
keywords = "A1.Stresses, A3. Molecular beam epitaxy, B1. Nanomaterials, B2. Topological insulator, B2. Semiconducting mercury compounds",
abstract = "Particularities of Molecular Beam Epitaxial (MBE) technology for the growth of Topological Insulators (TI) based on the semi-metal Hg1-xCdxTe are presented. A series of strained layers grown on GaAs substrates with a composition close to the 3D Dirac point were studied. The composition of the layers was verified by means of the position of the E1 maximum in optical reflectivity in the visible region. The surface morphology was determined via atomic force and electron microscopy. Magneto-transport measurements show quantized Hall resistance curves and Shubnikov de Hass oscillations (up to 50 K). It has been demonstrated that a well-developed MBE technology enables one to grow strained Hg1-xCdxTe layers on GaAs/CdTe substrates with a well-defined composition near the 3D Dirac point and consequently allows one to produce a 3D topological Dirac semimetal - 3D analogy of graphene - for future applications."
}
@article{HUANG2020105348,
title = "Flexible manipulation of topologically protected waves in one-dimensional soft periodic plates",
journal = "International Journal of Mechanical Sciences",
volume = "170",
pages = "105348",
year = "2020",
issn = "0020-7403",
doi = "https://doi.org/10.1016/j.ijmecsci.2019.105348",
url = "http://www.sciencedirect.com/science/article/pii/S0020740319324245",
author = "Yilan Huang and Yang Huang and Weiqiu Chen and Ronghao Bao",
keywords = "Periodic structure, Topologically protected, Interface state, Wave manipulation, Large deformation",
abstract = "In this paper, we investigate the possibility of flexible manipulation of elastic waves propagating in soft periodic plates through topological state shifting. We design a soft 1D phononic crystal by connecting two different periodic plates made of hyperelastic materials. By choosing different geometrical parameters of the two plates, topologically protected state of elastic waves is observed at the interface between them. Since the hyperelastic material can undergo large elastic deformation, flexible and efficient shifting of topological state can be realized by applying appropriate pre-stretch on the structure. The interface state wave modes can be either activated or deactivated by an applied pre-stretch on the structures with different initial geometrical parameters. Due to the advantageous property that topologically protected wave modes are stable against any defects and disorders, it provides a robust way of manipulating waves propagation in real time. The system and the strategy proposed here have great potential in constructing various novel acoustic devices."
}
@article{MOURRAIN2002612,
title = "On the Complexity of Isolating Real Roots and Computing with Certainty the Topological Degree",
journal = "Journal of Complexity",
volume = "18",
number = "2",
pages = "612 - 640",
year = "2002",
issn = "0885-064X",
doi = "https://doi.org/10.1006/jcom.2001.0636",
url = "http://www.sciencedirect.com/science/article/pii/S0885064X01906363",
author = "B. Mourrain and M.N. Vrahatis and J.C. Yakoubsohn",
keywords = "topological degree, -splines, Bézier curves, zero isolation, locating and computing roots, sign determination, generalized bisection, characteristic bisection",
abstract = "In this contribution the isolation of real roots and the computation of the topological degree in two dimensions are considered and their complexity is analyzed. In particular, we apply Stenger's degree computational method by splitting properly the boundary of the given region to obtain a sequence of subintervals along the boundary that forms a sufficient refinement. To this end, we properly approximate the function using univariate polynomials. Then we isolate each one of the zeros of these polynomials on the boundary of the given region in various subintervals so that these subintervals form a sufficiently refined boundary."
}
